State-of-the-Art Calculations of the 3d Transition-Metal Dimers: Mn₂ and Sc₂

Abstract

The problem of calculation of the electronic structure of transition-metal clusters (even dimers) still presents a challenge for computational chemistry. The reason is that the expansion of the ground state wave function on electronic configurations does not contain a principal configuration and a large number of reference configurations must be treated equally. Thus the multireference (MR) approaches are, in general, mandatory.

According to our studies of Mn₂ by the MRCISD(+Q)/aug-cc-pVQZ and ACPF approaches, the ground state is the singlet, ${\text{X}}{}^1\Sigma_{\text{g}}^{+}$, with the binding energy D _e = 1.7 kcal/mol (0.07 eV) and R _e = 3.6 Å. It was proved that the binding in the Mn₂ dimer is of the van der Waals type. The calculation of Sc₂ at the MRCISD(+Q)/cc-pV5Z level, showed that its ground state corresponds to a quintet, ${}^5\Sigma_{\text{u}}^{-}$, in agreement with experiment and previous precise calculations. The triplet ${}^3\Sigma_{\text{u}}^{-}$ state is located about 1.1 kcal/mol above. The ground state, ${\text{X}}{}^5\Sigma_{\text{u}}^{-}$, of the Sc₂ dimer was calculated by the MRCISD(+Q) method at the complete basis set (CBS) limit. This is the first MRCISD(+Q) calculation of 3d transition-metal clusters at the CBS limit. From the Mulliken population analysis and comparison with atomic energies follows that in the ground state Sc₂ dissociates on one Sc in the ground state and the other in the second excited quartet state, ⁴F_u. The spectroscopic parameters of the ground potential curve, obtained by the Dunham analysis at the valence MRCISD(+Q)/CBS level, are: R _e = 5.20 bohr, D _e = 50.37 kcal/mol, and ω _e = 234.5 cm⁻¹. The obtained value for the harmonic frequency agrees very well with the experimental one, ω _e = 239.9 cm⁻¹. The Sc₂ dimer is stabilized by the covalent bonding on the hybrid atomic orbitals.